Question 3 Adult respiratory distress syndrome (ARDS) is a complication in many critically ill patients. Rocker and coworkers¹ developed a logistic regression model for predicting ARDS in a patient based on three variables: ● ● PI Protein accumulation index. O Arterial oxygen in kPa. ● A Age in years. Some of the output from the SPSS calculation for this model is given below. Omnibus Testª Parameter (Intercept) Likelihood Ratio Chi- Square 58.418 Protein Accumulation Index 3 Dependent Variable: ARDS Model: (Intercept), Protein Accumulation Index, Arterial Oxygen / kPa, Age / years a. Compares the fitted model against the intercept-only model. df B 6.649 1.554 -.498 -.057 1ª Std. Error 2.2453 4371 Sig. .1631 .0257 .000 Lower 95% Wald Confidence Interval 2.249 .697 Parameter Estimates Arterial Oxygen/kPa Age / years (Scale) Dependent Variable: ARDS Model: (Intercept), Protein Accumulation Index, Arterial Oxygen / kPa, Age / years a. Fixed at the displayed value. -.818 -.107 Upper 11.050 2.411 -.179 -.006 Source (Intercept) Protein Accumulation Index Arterial Oxygen/kPa Age / years Dependent Variable: ARDS Model: (Intercept), Protein Accumulation Index, Arterial Oxygen / kPa, Age / years Hypothesis Test Wald Chi- Square Tests of Model Effects 8.770 12.643 9.330 4.848 df 1 1 Wald Chi- Square 1 1 8.770 12.643 9.330 4.848 Sig. Type III df .002 .028 Exp(B) .003 772.219 .000 4.731 .608 .945 1 1 Sig. 1 1 .003 .000 .002 .028 95% Wald Confidence Interval for Exp(B) Lower 9.474 2.009 .441 .898 a) Comment on the overall significance of the model. b) Comment on whether or not there is there evidence that the Protein Accumulation Index is associated with ARDS. Upper 62941.590 11.143 c) By considering the model coefficients, comment on how each of the three variables affects the probability of a patient having ARDS. .837 .994
Question 3 Adult respiratory distress syndrome (ARDS) is a complication in many critically ill patients. Rocker and coworkers¹ developed a logistic regression model for predicting ARDS in a patient based on three variables: ● ● PI Protein accumulation index. O Arterial oxygen in kPa. ● A Age in years. Some of the output from the SPSS calculation for this model is given below. Omnibus Testª Parameter (Intercept) Likelihood Ratio Chi- Square 58.418 Protein Accumulation Index 3 Dependent Variable: ARDS Model: (Intercept), Protein Accumulation Index, Arterial Oxygen / kPa, Age / years a. Compares the fitted model against the intercept-only model. df B 6.649 1.554 -.498 -.057 1ª Std. Error 2.2453 4371 Sig. .1631 .0257 .000 Lower 95% Wald Confidence Interval 2.249 .697 Parameter Estimates Arterial Oxygen/kPa Age / years (Scale) Dependent Variable: ARDS Model: (Intercept), Protein Accumulation Index, Arterial Oxygen / kPa, Age / years a. Fixed at the displayed value. -.818 -.107 Upper 11.050 2.411 -.179 -.006 Source (Intercept) Protein Accumulation Index Arterial Oxygen/kPa Age / years Dependent Variable: ARDS Model: (Intercept), Protein Accumulation Index, Arterial Oxygen / kPa, Age / years Hypothesis Test Wald Chi- Square Tests of Model Effects 8.770 12.643 9.330 4.848 df 1 1 Wald Chi- Square 1 1 8.770 12.643 9.330 4.848 Sig. Type III df .002 .028 Exp(B) .003 772.219 .000 4.731 .608 .945 1 1 Sig. 1 1 .003 .000 .002 .028 95% Wald Confidence Interval for Exp(B) Lower 9.474 2.009 .441 .898 a) Comment on the overall significance of the model. b) Comment on whether or not there is there evidence that the Protein Accumulation Index is associated with ARDS. Upper 62941.590 11.143 c) By considering the model coefficients, comment on how each of the three variables affects the probability of a patient having ARDS. .837 .994
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Transcribed Image Text:Question 3
Adult respiratory distress syndrome (ARDS) is a complication in many critically ill patients. Rocker and
coworkers¹ developed a logistic regression model for predicting ARDS in a patient based on three variables:
PI Protein accumulation index.
O Arterial oxygen in kPa.
A Age in years.
Some of the output from the SPSS calculation for this model is given below.
Omnibus Testª
●
●
●
Likelihood
Ratio Chi-
Square
58.418
3
Dependent Variable: ARDS
Model: (Intercept), Protein
Accumulation Index, Arterial Oxygen /
kPa, Age / years
df
a. Compares the fitted model
against the intercept-only
model.
B
6.649
1.554
-.498
-.057
1ª
Std. Error
2.2453
.4371
Sig.
.000
.1631
.0257
Lower
Parameter
(Intercept)
Protein Accumulation
Index
Arterial Oxygen/kPa
Age / years
(Scale)
Dependent Variable: ARDS
Model: (Intercept), Protein Accumulation Index, Arterial Oxygen / kPa, Age / years
a. Fixed at the displayed value.
95% Wald Confidence Interval
2.249
.697
-.818
-.107
Parameter Estimates
Upper
Source
(Intercept)
Protein Accumulation
Index
11.050
2.411
-.179
-.006
Tests of Model Effects
Hypothesis Test
Wald Chi-
Square
8.770
12.643
Arterial Oxygen/kPa
Age / years
Dependent Variable: ARDS
Model: (Intercept), Protein Accumulation Index, Arterial Oxygen / kPa,
Age / years
9.330
4.848
df
1
1
Wald Chi-
Square
1
1
8.770
12.643
9.330
4.848
Sig.
.003
.000
Type III
.002
.028
df
Exp (B)
772.219
4.731
1
1
.608
.945
1
Sig.
1
.003
.000
.002
.028
95% Wald Confidence Interval
for Exp(B)
Lower
9.474
2.009
.441
.898
a) Comment on the overall significance of the model.
b) Comment on whether or not there is there evidence that the Protein Accumulation Index is
associated with ARDS.
Upper
62941.590
11.143
c) By considering the model coefficients, comment on how each of the three variables affects the
probability of a patient having ARDS.
.837
.994
Transcribed Image Text:d) The odds of a patient having ARDS, , are related to the model through the following equation:
(1Pp)
In Ω = ln
ii)
=
= bo + b₁PI + b₂0 + b3 A
where P is the probability of a patient having ARDS. Using the coefficients from the SPSS output,
determine
i)
The odds, n, that a 65-year-old patient with low arterial oxygen, 6 kPa, and high protein
index, 5.5, has ARDS.
The odds, 22, that a 65-year-old patient with high arterial oxygen, 20 kPa, and low protein
index, 0.2, has ARDS.
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